# Stored data for newform 42.2.d.a, downloaded from the LMFDB on 20 April 2024.
{"label": "42.2.d.a", "space_label": "42.2.d", "level": 42, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 206191984682, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2304.2", "trace_hash": 1198725219951304269, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q-\\beta _{2}q^{2}+\\beta _{1}q^{3}-q^{4}+(-\\beta _{1}+\\beta _{3})q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 21, "char_orbit_label": "d", "char_is_real": true, "Nk2": 168, "analytic_conductor": 0.3353716884893776, "hecke_ring_index": 1, "level_radical": 42, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.763", "prec": 17}, "analytic_rank_proved": true, "char_values": [42, 2, [29, 31], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [41], "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.764", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "119.466", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4665.047", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, -4], "traces": [0, 4, 0, 0, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -12, 4, 0, 12, 0, 0, 12, 0, 0, 0, 4, 0, 0, 4, 0, -12, 0, 0, 0, 0, 0, 0, -8, 0, -12, 0, 0, -12, 16, 0, 0, -24, 0, 0, -20, 0, 24, 0, 0, 0, 0, 0, 12, 24, 0, 12, 0, 0, 0, -4, 0, 0, 32, 0, 0, 24, 0, -12, 0, 0, 0, 0, 0, 12, -40, 0, -36, 0, 0, -12, -48, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 24, 0, 0, 12, -24, 0, 0, 40, 0, 0, -4, 0, -12, 0, 0, 0, 0, 0, 12, 44, 0, -24, 0, 0, -12, 32, 0, 0, -24, 0, 0, -24, 0, 36, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -24, 8, 0, 0, -32, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 12, 28, 0, 0, -16, 0, 0, -4, 0, -60, 0, 0, 0, 0, 0, -60, 24, 0, 0, 0, 0, 36, 24, 0, 0, 16, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, -24, 48, 0, 72, 0, 0, 12, -32, 0, 0, 48, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, -24, 0, -12, 0, 0, 0, -24, 0, 0, -48, 0, 0, -48, 0, -12, 0, 0, 0, 0, 0, -24, 24, 0, 12, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 0, -72, 0, 0, 0, 0, 0, 0, -32, 0, -36, 0, 0, 12, 48, 0, 0, -88, 0, 0, -24, 0, 24, 0, 0, 0, 0, 0, 12, 28, 0, 24, 0, 0, 24, 120, 0, 0, 24, 0, 0, -16, 0, 36, 0, 0, 0, 0, 0, 48, 0, 0, -12, 0, 0, -72, 40, 0, 0, 0, 0, 0, 24, 0, 36, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 12, -128, 0, 0, 48, 0, 0, 68, 0, -72, 0, 0, 0, 0, 0, -36, 0, 0, -60, 0, 0, -24, -96, 0, 0, 52, 0, 0, -24, 0, 60, 0, 0, 0, 0, 0, 0, 56, 0, 48, 0, 0, 36, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, -72, 0, 0, 0, 0, -12, 4, 0, 0, 0, 0, 0, -24, 0, -24, 0, 0, 0, 0, 0, 0, -24, 0, 12, 0, 0, -12, 8, 0, 0, 24, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 72, -40, 0, -48, 0, 0, 0, 48, 0, 0, 0, 0, 0, 4, 0, 12, 0, 0, 0, 0, 0, 12, 112, 0, -72, 0, 0, 0, 56, 0, 0, 96, 0, 0, -32, 0, -36, 0, 0, 0, 0, 0, 72, 24, 0, -12, 0, 0, -72, -44, 0, 0, -128, 0, 0, -48, 0, 24, 0, 0, 0, 0, 0, 12, -80, 0, 24, 0, 0, 12, -72, 0, 0, -32, 0, 0, -96, 0, 36, 0, 0, 0, 0, 0, -108, 24, 0, 0, 0, 0, 12, 96, 0, 0, -52, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -36, 8, 0, 60, 0, 0, -12, 32, 0, 0, 0, 0, 0, 40, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 36, 0, 0, 0, 128, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 72, 0, 0, 24, 0, 0, 0, -8, 0, 0, 48, 0, -48, 0, 0, 0, 0, 0, 0, 32, 0, 36, 0, 0, 72, -120, 0, 0, 56, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, -12, -116, 0, 0, 0, 0, 0, 8, 0, 0, -72, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -48, -48, 0, 0, 0, 0, 0, 64, 0, 0, -72, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -24, 144, 0, -72, 0, 0, -12, 136, 0, 0, -28, 0, 0, -48, 0, -36, 0, 0, 0, 0, 0, -108, 16, 0, 72, 0, 0, 0, 48, 0, 0, -96, 0, 0, 4, 0, -36, 0, 0, 0, 0, 0, 60, 40, 0, 0, 0, 0, -24, 0, 0, 0, 24, 0, 0, -96, 0, 120, 0, 0, 0, 0, 0, 0, 96, 0, 60, 0, 0, 60, -24, 0, 0, 80, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 48, -32, 0, -84, 0, 0, -36, -8, 0, 0, -24, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 144, -16, 0, 48, 0, 0, -24, 24, 0, 0, 0, 0, 0, -20, 0, 36, 0, 0, 0, 0, 0, 0, -120, 0, -72, 0, 0, 12, 96, 0, 0, -120, 0, 0, 144, 0, -60, 0, 0, 0, 0, 0, -120, 0, 0, 24, 0, 0, 0, -48, 0, 0, 56, 0, 0, 120, 0, -72, 0, 0, 0, 0, 0, -12, -48, 0, 0, 0, 0, -12, -28, 0, 0, 32, 0, 0, -44, 0, 108, 0, 0, 0, 0, 0, -72, -48, 0, 0, 0, 0, 24, -120, 0, 0, 216, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, -48, -88, 0, 12, 0, 0, -60, -224, 0, 0, -144, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 72, 144, 0, 0, 0, 0, 48, 24, 0, 0, 112, 0, 0, 24, 0, 12, 0, 0, 0, 0, 0, 72, 40, 0, -36, 0, 0, 0, -8, 0, 0, 24, 0, 0, 48, 0, 96, 0, 0, 0, 0, 0, 168, 48, 0, 36, 0, 0, -36, 0, 0, 0, 96, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 12, 124, 0, -144, 0, 0, -72, 32, 0, 0, 48, 0, 0, -24, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, -24, -24, 0, 0, -152, 0, 0, 0, 0, -12, 0, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 7, 2, -1, 2, 0], [1, 1, 21, 3, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 3, "minimal_twist": "42.2.d.a", "char_is_minimal": true, "conrey_index": 41, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, -1, 0], [0, 1, 0, 0], [-1, 0, 0, 0], [0, -1, 0, 1], [0, 0, 0, -1], [-1, -1, 0, -1], [0, 0, 1, 0], [0, 0, 3, 0], [0, 1, 0, 1], [0, 0, 0, 0], [0, -1, 0, 0], [0, 1, 0, 1], [0, -1, 1, 1], [-3, 0, -3, 0], [1, 0, 0, 0], [0, 2, 0, -2], [3, 0, 0, 0], [0, -1, 0, -1], [0, 1, 0, -1], [3, -1, -3, 0], [0, 0, 0, 0], [0, 0, -6, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 1, 0, -1], [0, 0, 0, 3], [1, 1, 0, 1], [0, 0, 6, 0], [-3, 0, 3, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [0, -2, 0, -2], [0, 1, 6, -1], [0, 0, -3, 0], [-2, 0, 0, 0], [0, -1, 0, 1], [-3, 0, 3, 0], [0, -1, 0, -1], [0, -2, 0, 2], [-3, 0, -3, 1], [4, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, -3], [-6, 0, 0, 0], [0, 2, 0, -2], [0, 1, 0, 0], [-5, 2, 0, 2], [0, 0, -1, 0], [6, 0, 6, 0], [0, -1, 0, -1], [0, 0, -6, 0], [0, 3, 0, 0], [0, 0, 0, 0], [0, 1, -1, -1], [3, 0, -3, 0], [6, 0, 0, 0], [0, -5, 0, 5], [3, 0, 3, 0], [0, 5, 0, 5], [0, 0, 0, 0], [0, 3, -3, -3], [-1, 0, 0, 0], [0, 0, -6, 0], [0, 0, 0, 0], [8, 0, 0, 0], [0, -2, 0, 2], [0, 0, 0, -6], [6, -1, 0, -1], [0, 0, 0, 0], [-3, 0, 0, 0], [0, -4, 0, -4], [0, 0, 2, 0], [0, 1, 0, 0], [0, 1, 0, 1], [0, 0, 0, 0], [3, 0, 3, 0], [-10, 0, 0, 0], [0, -1, 0, 1], [-9, 0, 0, 0], [0, 2, 0, 2], [0, 1, 0, -1], [-3, 1, 3, 0], [-12, 0, 0, 0], [0, 0, -4, 0], [0, 0, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, 3], [6, -1, 0, -1], [0, 0, 6, 0], [0, 0, 0, 0], [0, -2, 0, -2], [0, 0, 6, 0], [0, 0, 0, -1], [0, -2, 0, -2], [0, 2, 5, -2], [0, 0, 0, 0], [-1, 0, 0, 0]]}